Francis Bonahon and Helen Wong

Abstract

We relate two different quantizations of the character variety consisting of all representations of
surface groups in SL2.
One is the Kauffman skein algebra considered by Bullock, Frohman and
Kania-Bartoszyńska, Przytycki and Sikora, and Turaev. The other is the quantum
Teichmüller space introduced by Chekhov and Fock and by Kashaev. We construct
a homomorphism from the skein algebra to the quantum Teichmüller space which,
when restricted to the classical case, corresponds to the equivalence between these
two algebras through trace functions.